# ID 1
blah blah
blah blah
$ description 1
blah blah
# ID 2
blah
$ description 2
blah blah
blah blah

# ID 1
$ description 1
blah blah
# ID 2
$ description 2
blah blah
blah blah

sed '/^#/,/^$/{/^#/!{/^$/!d}}' file.txt

# ID 1
$ description 1
blah blah
# ID 2
$ description 2
blah blah
blah blah

$ cat test
1
start
2
end
3
$ sed -n '1,/start/p;/end/,$p' test
1
start
end
3
$ sed '/start/,/end/d' test
1
3

sed -n -e "1,/# ID 1/ p" -e "/$ description 1/,$ p"

sed '/^#/,/^$/{//!d;};' file